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Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible, less likely, equally likely (even chance), more likely, certain. Give reasons why you gave each event its ranking.
A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts: 10 red | 8 green | 7 yellow | 5 blue
A survey is conducted at a school where a random sample of 40 students is asked about their favourite club. The responses are: 14 Science | 11 Arts | 9 Sports | 6 Debate. Assume there are 800 students in the whole school.
What is the probability of getting an even number when rolling a fair 6-sided die?
Answer: The possible outcomes are $\{1, 2, 3, 4, 5, 6\}$.
The even numbers are $\{2, 4, 6\}$.
Probability = Number of favourable outcomes / Total possible outcomes = $3 / 6 = \mathbf{1/2}$ (or $0.5$).
Suppose you roll a 6-sided die 12 times and get a '3' three times.
When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
Answer: The total number of possible outcomes (the sample size) is 6. The sample space is $\{1, 2, 3, 4, 5, 6\}$.
For the following experiments write down the sample space S.
In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.
There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.
Fill in the blanks.
Write the sample space and calculate the probability based on the given information.
A child has 2 shirts (one red and one blue) and 3 types of pants (jeans, khakis, and shorts). List all the possible combinations of outfits consisting of one shirt and one pair of pants. Display your answer in a table format.
| Shirt | Pants | Outfit Combination |
|---|---|---|
| Red | Jeans | Red & Jeans |
| Red | Khakis | Red & Khakis |
| Red | Shorts | Red & Shorts |
| Blue | Jeans | Blue & Jeans |
| Blue | Khakis | Blue & Khakis |
| Blue | Shorts | Blue & Shorts |
A tyre company records distances before replacement in 1000 cases.
| Distance (km) | Less than 4000 | 4001 to 9000 | 9001 to 14000 | More than 14000 |
|---|---|---|---|---|
| Number of cases | 20 | 210 | 325 | 445 |
Find the probability that a randomly chosen tyre lasts:
(i) Less than 4000 km.
(ii) Between 4000 and 14000 km.
(iii) More than 14000 km.
The letters of the word 'PEACE' are placed on cards. Leela draws a card without looking.
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at
A basket contains 4 red balls and 5 blue balls. One ball is drawn and laid aside, and a second ball is drawn. Draw a tree diagram to represent the possible outcomes and probabilities. Use the tree diagram to answer the following questions.
Answer:
Tree Diagram Construction:
First draw: P(Red) = 4/9, P(Blue) = 5/9.
Second draw (without replacement, total is now 8 balls):
- If Red was drawn first: P(Red) = 3/8, P(Blue) = 5/8.
- If Blue was drawn first: P(Red) = 4/8, P(Blue) = 4/8.
(i) P(Red then Blue) = P(Red first) $\times$ P(Blue second | Red first) = $(4/9) \times (5/8) = 20/72 = \mathbf{5/18}$.
(ii) P(Blue then Blue) = P(Blue first) $\times$ P(Blue second | Blue first) = $(5/9) \times (4/8) = 20/72 = \mathbf{5/18}$.
Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for this experiment? Why do the other lists fail to qualify as a sample space?
Answer: The correct list is (iv) {0, 1, 2, 3}. When tossing three coins, you can get 0 heads (TTT), 1 head (HTT, THT, TTH), 2 heads (HHT, HTH, THH), or 3 heads (HHH).
The other lists fail because:
(i) It omits the possibility of getting 0 heads.
(ii) It omits the possibility of getting 3 heads.
(iii) It includes 4 heads, which is impossible when only tossing three coins.
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